Propagation of Longitudinal Stress Waves in Elastic and Linearly Viscoelastic Bars of Variable Cross-Section

摘要

The propagation of longitudinal stress waves in elastic and linearly viscoelastic bars of slowly varying cross-section, is treated by an elementary theory. Exact solutions based on this theory are presented for cones and exponentially variable cross-sections. An approximate solution which is valid in certain regions of the bar is derived for a general bar of slowly varying cross-section. According to this solution, the amplitude of the displacement wave is inversely proportional to the square root of the local cross-sectional area of the bar. (In viscoelastic bars, the amplitude is also decaying exponentially due to the internal friction in the bar). The effect of radial inertia on the propagation of longitudinal stress waves in elastic cones is also discussed in this report. It is found that the phase velocity of the waves is dependent on the wavelength and the local radius of the cone. This phase velocity is represented by an expression which is similar to that derived by Rayleigh for the case of a cylindrical bar of uniform cross-section. Another problem which is treated in this report is the reflection of stress waves at the interface between two elastic or viscoelastic cones attached end to end. It is found that during reflection, changes in pulse shapes occur, both in the elastic and the viscoelastic cases. (Author)